These functions are trivially computed in terms of other elliptic integrals
and generally have very low error rates (a few epsilon) unless parameter
φ
is very large, in which case the usual trigonometric function argument-reduction
issues apply.

The tests use a mixture of spot test values calculated using values calculated
at wolframalpha.com, and random test data generated using MPFR at 1000-bit
precision and a deliberately naive implementation in terms of the Legendre
integrals.